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CGI Sample Problems

First Grade-  Mrs. Kent had some boxes of tissues at the beginning of the school year.  The students used 10 boxes.  Now she has 15 boxes left.  How many boxes of tissues did Mrs. Kent have at the beginning of the school year?

Third Grade- Nineteen children are taking a mini-bus to the zoo.  They will have to sit either 2 or 3 to a seat.  The bus has seven seats.  How many children will have to sit three to a seat, and how many can sit two to a seat?

Fifth Grade- I have 18 yards of ribbon.  It takes 2 1/4 yards of ribbon to make one bow.  How many bows can I make using the ribbon I have?

Cognitively Guided Instruction (CGI)

Cognitively Guided Instruction (CGI) is a professional development program based on an integrated approach of research focused on

(a) the development of students’ mathematical thinking;

(b) instruction that influences that development;

(c) teachers’ knowledge and beliefs that influence their instructional practices; and

(d) the way that teachers’ knowledge, beliefs, and practices are influenced by their understanding of students’ mathematical thinking.

Using CGI strategies is an effective way of implementing the Common Core Curriculum for Mathematics at the elementary level.  Studies have consistently demonstrated that Cognitively Guided Instruction (CGI) students show significant gains in problem solving. These gains reflect the emphasis on problem solving in CGI classes. Learning to understand the development of children’s mathematical thinking can lead to fundamental changes in teachers’ beliefs and practices. These changes were reflected in students’ learning.

The goals of CGI are:

  1. Analyze story problems and number sentences to determine their mathematical demands and recognize student responses in terms of cognitive development.
  2. Assess students’ thinking and design problems that will develop students’ understanding of concepts and skills.
  3. Facilitate discussions that provide a window into children’s thinking, strengthen children’s ability to reason about arithmetic, and build their capacity for algebraic reasoning.
  4. Use open and true/false number sentences to develop students’ understanding of mathematical concepts and skills.
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